In an open quantum system with parity-time symmetry, the Hamiltonian is non-Hermitian but possesses purely real eigenvalues. Once the parity-time (PT) symmetry is broken, the eigenvalues are no longer real and become complex. During this time, the eigenvalues and eigenfunctions of the Hamiltonian coalesce and the exceptional points (EPs) may emerge. The EPs have been investigated in PT symmetric multilayer structure. In fact, the formation of EPs requires only non-Hermiticity and the PT symmetry is not necessary. Recently, metamaterials are also shown to be a proper platform to study EPs. But the previous work only find one EP and reveal unidirectional reflectionless light transport as the light is incident from one side of the system. And the topological properties of EPs are not comprehensively studied.
The ultrafast optics group led by Prof. Peixiang Lu investigates the optical exceptional points (EPs) in a graphene incorporated multilayer metamaterial which manifests Fano resonance. The optical property of metamaterial can be tuned flexibly by modulating the chemical potential of graphene. In the aid of Fano resonance, they find two zero reflection points, which yield two EPs in the proposed structure. Moreover, the topological structure of EP is studied. Two eigenvalues of the scattering matrix are interchanged while encircling an EP in parameter space and the eigenvalues show changes of level crossing and anti-crossing in the vicinity of EP. This work makes a significant sense to research of EPs.
This work is published on Opt. Express Vol. 25, No. 7, 7203-7212 (2017). This work was supported by Program 973 (2014CB921301); National Natural Science Foundation of China (NSFC) (11304108, 11674117); Natural Science Foundation of Hubei Province (2015CFA040).
Figure Eigenvalues s1,2 as a function of incident wavelength λ and chemical potential of graphene μc. The black arrows point to the positions of EP1 and EP2.